Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes, while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is:

Question

Accepted Answer

1. **Understanding the Problem:**  
   - Train A takes 10 minutes to travel from X to Y.  
   - Train B takes 9 minutes to reach X after meeting Train A at point M.  
   - Both trains start at the same time and travel at constant speeds.

2. **Key Observations:**  
   - Let the time taken by Train A to reach M be $$t$$ minutes. Then Train B also takes $$t$$ minutes to reach M from Y (since they meet at the same time).  
   - The remaining time for Train A to travel from M to Y is $$10 - t$$ minutes.  
   - Similarly, the remaining time for Train B to travel from M to X is $$9$$ minutes.

3. **Using the Ratio of Speeds:**  
   Since both trains cover equal distances between M and their respective destinations:  
   $$
   \frac{t}{10 - t} = \frac{10 - t}{9}.
   $$

4. **Solving for $$t$$:**  
   Cross-multiply:  
   $$
   t(9) = (10 - t)(10 - t).
   $$  
   Expand:  
   $$
   t^2 + 15t - 90 = 0.
   $$  
   Factorize:  
   $$
   (t + 15)(t - 6) = 0.
   $$  
   Since time cannot be negative, $$t = 6$$.

5. **Total Time for Train B:**  
   The time taken by Train B to travel from Y to M is $$t = 6$$ minutes, and from M to X is $$9$$ minutes. Thus, the total time is:  
   $$
   6 + 9 = 15 	ext{ minutes}.
   $$

Hence, the correct answer is **A. 15**.

Answer

Answer

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